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Claude Finds 3D Counterexample to Jacobi Conjecture, Unsolved Since 1939
According to monitoring by Beating, Anthropic mathematician Levent Alpöge used Claude Fable to discover a three-dimensional counterexample to the Jacobi conjecture, an unsolved problem since 1939. The model produced a polynomial mapping with constant Jacobian determinant of −2 that maps three distinct inputs to the same output, proving it cannot be invertible in three and higher dimensions. OpenAI researcher Aaron Lou independently verified the result using internal Codex, which discovered an es
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